Average Error: 18.7 → 11.5
Time: 6.6s
Precision: binary64
\[[V, l]=\mathsf{sort}([V, l])\]
\[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]
↓
\[\begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -3.377932146154755 \cdot 10^{-185}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 1.576643 \cdot 10^{-318}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 3.4837495983208395 \cdot 10^{+302}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]
c0 \cdot \sqrt{\frac{A}{V \cdot \ell}}
↓
\begin{array}{l}
\mathbf{if}\;V \cdot \ell \leq -3.377932146154755 \cdot 10^{-185}:\\
\;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\

\mathbf{elif}\;V \cdot \ell \leq 1.576643 \cdot 10^{-318}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\

\mathbf{elif}\;V \cdot \ell \leq 3.4837495983208395 \cdot 10^{+302}:\\
\;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\

\mathbf{else}:\\
\;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\\


\end{array}

(FPCore (c0 A V l) :precision binary64 (* c0 (sqrt (/ A (* V l)))))
↓
(FPCore (c0 A V l)
 :precision binary64
 (if (<= (* V l) -3.377932146154755e-185)
   (* c0 (sqrt (* A (/ 1.0 (* V l)))))
   (if (<= (* V l) 1.576643e-318)
     (* c0 (sqrt (/ (/ A V) l)))
     (if (<= (* V l) 3.4837495983208395e+302)
       (* c0 (/ (sqrt A) (sqrt (* V l))))
       (* c0 (sqrt (/ 1.0 (/ V (/ A l)))))))))
double code(double c0, double A, double V, double l) {
	return c0 * sqrt(A / (V * l));
}
↓
double code(double c0, double A, double V, double l) {
	double tmp;
	if ((V * l) <= -3.377932146154755e-185) {
		tmp = c0 * sqrt(A * (1.0 / (V * l)));
	} else if ((V * l) <= 1.576643e-318) {
		tmp = c0 * sqrt((A / V) / l);
	} else if ((V * l) <= 3.4837495983208395e+302) {
		tmp = c0 * (sqrt(A) / sqrt(V * l));
	} else {
		tmp = c0 * sqrt(1.0 / (V / (A / l)));
	}
	return tmp;
}

Error

Bits error versus c0

Bits error versus A

Bits error versus V

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (*.f64 V l) < -3.37793214615475482e-185

    1. Initial program 13.6

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied div-inv_binary6413.6

      \[\leadsto c0 \cdot \sqrt{\color{blue}{A \cdot \frac{1}{V \cdot \ell}}} \]

    if -3.37793214615475482e-185 < (*.f64 V l) < 1.5766425e-318

    1. Initial program 46.5

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied associate-/r*_binary6432.2

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{\frac{A}{V}}{\ell}}} \]

    if 1.5766425e-318 < (*.f64 V l) < 3.48374959832083955e302

    1. Initial program 10.4

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied sqrt-div_binary640.5

      \[\leadsto c0 \cdot \color{blue}{\frac{\sqrt{A}}{\sqrt{V \cdot \ell}}} \]

    if 3.48374959832083955e302 < (*.f64 V l)

    1. Initial program 41.1

      \[c0 \cdot \sqrt{\frac{A}{V \cdot \ell}} \]

    2. Applied clear-num_binary6441.1

      \[\leadsto c0 \cdot \sqrt{\color{blue}{\frac{1}{\frac{V \cdot \ell}{A}}}} \]

    3. Simplified21.6

      \[\leadsto c0 \cdot \sqrt{\frac{1}{\color{blue}{\frac{V}{\frac{A}{\ell}}}}} \]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;V \cdot \ell \leq -3.377932146154755 \cdot 10^{-185}:\\ \;\;\;\;c0 \cdot \sqrt{A \cdot \frac{1}{V \cdot \ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 1.576643 \cdot 10^{-318}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{\frac{A}{V}}{\ell}}\\ \mathbf{elif}\;V \cdot \ell \leq 3.4837495983208395 \cdot 10^{+302}:\\ \;\;\;\;c0 \cdot \frac{\sqrt{A}}{\sqrt{V \cdot \ell}}\\ \mathbf{else}:\\ \;\;\;\;c0 \cdot \sqrt{\frac{1}{\frac{V}{\frac{A}{\ell}}}}\\ \end{array} \]

Reproduce

herbie shell --seed 2022020 
(FPCore (c0 A V l)
  :name "Henrywood and Agarwal, Equation (3)"
  :precision binary64
  (* c0 (sqrt (/ A (* V l)))))